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Infinite dimensional rotations and Laplacians in terms of white noise calculus

Published online by Cambridge University Press:  22 January 2016

Takeyuki Hida ,
Nobuaki Obata  and
Kimiaki Saitô
Takeyuki Hida
Affiliation:
Department of Mathematics, Meijo University, Nagoya 468, Japan
Nobuaki Obata
Affiliation:
Department of Mathematics, School of Science, Nagoya University, Nagoya 464-01, Japan
Kimiaki Saitô
Affiliation:
Department of Mathematics, School of Science, Nagoya University, Nagoya 464-01, Japan
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The theory of generalized white noise functionals (white noise calculus) initiated in [2] has been considerably developed in recent years, in particular, toward applications to quantum physics, see e.g. [5], [7] and references cited therein. On the other hand, since H. Yoshizawa [4], [23] discussed an infinite dimensional rotation group to broaden the scope of an investigation of Brownian motion, there have been some attempts to introduce an idea of group theory into the white noise calculus. For example, conformal invariance of Brownian motion with multidimensional parameter space [6], variational calculus of white noise functionals [14], characterization of the Levy Laplacian [17] and so on.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 128 , December 1992 , pp. 65 - 93
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1992

References

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